Abstract
Abstract. This paper deals with bundle adjustment with constrained cameras, i.e. where the orientation of certain cameras is expressed relatively to others, and these relative orientations are part of the unknowns. Despite the remarkable interest for oblique multi-camera systems, an empirical study on the effect of enforcing relative orientation constraints in bundle adjustment is still missing. We provide experimental evidence that indeed these constraints improve the accuracy of the results, while reducing the computational load as well. Moreover, we report for the first time in the literature the complete derivation of the Jacobian matrix for bundle adjustment with constrained cameras, to foster other implementations.
Highlights
Over the past two decades almost all existing companies in the geospatial sector have opened up for oblique imaging technology and included multi-head oblique camera units in their portfolios
The only work, to the best of our knowledge, that analyses an implementation of bundle block adjustment (BBA) with relative orientation constraints and compares the results achieved with the custom BBA is (Sun et al, 2016), that states that this approach has a lower accuracy on the basis of experiments that report worse reprojection errors than in the case where the constraints are ignored
PROBLEM STATEMENT Let us consider an oblique multi-camera system composed by k cameras, where one is taken as the reference and the remaining k − 1 have a fixed but unknown relative orientation with respect to the first one
Summary
Over the past two decades almost all existing companies in the geospatial sector have opened up for oblique imaging technology and included multi-head oblique camera units in their portfolios. Either as stand-alone solutions (Remondino, Gerke, 2015) or more recently in combination with a LiDAR unit (Toschi et al, 2019), these oblique systems have expanded the potentialities of the area-wide mapping market towards a more complete and intuitive scene understating concept They offer the advantages of a slanted view geometry, that allows the potential 3D reconstruction of building facades and other urban vertical objects (Haala, Rothermel, 2015). The only work, to the best of our knowledge, that analyses an implementation of BBA with relative orientation constraints and compares the results achieved with the custom BBA is (Sun et al, 2016), that states that this approach has a lower accuracy on the basis of experiments that report worse reprojection errors than in the case where the constraints are ignored It must be said, though, that looking at the reprojection error without considering the degrees of freedom of the model being fitted may lead to biased conclusions. We will use the “matrix differential calculus” formalism (Magnus, Neudecker, 1999), which allows a compact and modular derivation
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